Such a heat exchanger is used as, for example, an oil cooler incorporating a heat exchanger core which comprises a plurality of plate pairs with each plate pair being constituted by two identical plates one of which is disposed in an inverted orientation relative to the other plate of the plate pair. In the heat exchanger core the plate pairs are disposed in stacked relationship, with a space between the plates of each plate pair constituting a flow path for, for example, engine oil between an oil inlet and an oil outlet, and with a space between each adjacent pair of plate pairs constituting a flow path for coolant between a coolant inlet and a coolant outlet. The heat exchanger core is disposed within the casing which may be of rectangular, such as substantially square, form and which comprises top and bottom cover walls mounted on the side wall, one or both of the cover walls having oil inlet and outlet openings in communication, respectively, with the oil inlet to the oil flow path between the plates of each plate pair and with the oil outlet from the oil flow path between the plates of each plate pair. The side wall of the casing has coolant inlet and outlet openings in communication, respectively, with the coolant inlet to the coolant flow path between the adjacent plates of each adjacent plate pair and with the coolant outlet from the coolant flow path between the adjacent plates of each adjacent plate pair.